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Permutations of finite fields for check digit systems. (English) Zbl 1248.11100
From the authors’ abstract: Let \(q\) be a prime power and \(n\) a positive divisor of \(q-1\). We prove an asymptotic formula for the number of polynomials \[ f(X)=\frac{a-b}{n}\bigg(\sum_{j=1}^{n-1} X^{j(q-1)/n}\bigg)X+\frac{a+b(n-1)}{n}\,X\in\mathbb{F}_q[X] \] such that the polynomials \(f(X)\), \(f(X)\pm X\), and \(f(f(X))\pm X\) are all permutation polynomials over \(\mathbb{F}_q\).

11T06 Polynomials over finite fields
11T22 Cyclotomy
11T71 Algebraic coding theory; cryptography (number-theoretic aspects)
Full Text: DOI
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